
Related to the above previous researches, we focus on the fact that the cylindrical square grid graphs are obtained from \(L_m\)  and \(C_n\)  by a certain “product” construction. As Harary [1]} mentioned, there are various ways to construct a graph structure on \(V(G_1) \times V(G_2)\)  for given two graphs \(G_1\)  and \(G_2\) . A cylindrical square grid graph is the Cartesian product of \(L_m\)  and \(C_n\)  for some \(m, n\) . In this paper, we are interested in the lexicographic product of two graphs, which is defined as follows.
